Further Proofs for the 1-Photon PathEntanglement Communications Scheme

The author had previously set out devices to communicate over space-like intervals, with a full proof for the 2‑photon device and only a partial proof for the 1-photon device. The 2-photon device exploits entangled pairs; the 1-photon device utilises path-entanglement. The 1-photon device is fully analysed, then similarities (and differences) are drawn to the 2-photon device to show the holes in the No-communications Theorem: the creation operators representing the sum of paths through the device can be mapped outside the device and quantum state reduction/measurement is a space-like operation. A common misconception on faux rank-3 systems made from rank-2 components is elucidated, avoiding the criticism and null result obtained by naively taking the partial trace.